The term "otaku" seems to have been introduced to anime fans in the US and other countries via Studio Gainax's "Otaku no Video 1985," a self-parody film.
Otaku, meaning probably "venerable house," refers to someone who has a devotion to a subject or hobby (not necessarily anime) to the point of not leaving home. For instance, an otaku fan of a particular movie star could quite possibly know all of the films s/he has been in, their birth date, time of birth, shoe size, favorite toothpaste, etc. Generally speaking, calling someone an otaku in Japan is an insult, implying that their social skills have atrophied or never even developed, due to their manic involvement in their chosen fandom.

In America, the term is used to denote a zealous fan, usually of anime and/or manga. Due to its introduction to most people's vocabulary through its tongue-in-cheek use in Gainax's film, "otaku" tends to have a much less dire definition overseas.

When dealing with Japanese people, however, it may be best to keep in mind the modern Japanese image of an otaku -- Someone who only leaves their home to eat or shop, if at all, with an overwhelming and unhealthy obsession about something. It can as easily refer to a stalker or sociopath as it can to a harmless anime buff.

Best to avoid the word altogether if one is not sure of the context in which it will be received.

Otaku is extremely negative in meaning as it is used to refer to someone who stays at home all the time and doesn't have a life (no social life, no love life, etc)

Usually an otaku person has nothing better to do with their life so they pass the time by watching anime, playing videogames, surfing the internet (otaku is also used to refer to a nerd/hacker/programmer).

In the Western culture, people confuse otaku to be something positive like "Guru". If you think about it, it's not really good to be called a guru if it means you are a total loser who can't socialize with other people except through the Internet.

Other Japanese words which have been confused by Westerners also include but not limited to: Anime, Manga, etc

The Urban Dictionary T-Shirt

A Japanese word describing a person beyond the realm of fandom but into mania that is improperly used by American fans.

In Japan the word "otaku" has become taboo because of Miyazaki Tsutomu who went on a toddler murdering spree in the 80's, video taping the young girls he had murdered from an obsession with lolicon (female pedophilic manga).

Americans use this term to call themselves "fanboys" or "fangirls" with almost no knowledge of the horrific roots behind the word.

American Fangirl: "I have a huge collection of Macross, NGE, Sailor Moon, yaoi, and many other anime! I'm such an otaku!"
Non-anime fan: "...Uhm, you do know about that word right?"

The Urban Dictionary T-Shirt

Otaku has multiple meanings. Casual anime fans use this word in the context of being a well established fan who knows much about anime and manga. Japanese see this term as derogitory which represents a person who is a lifeless nerd. Wapanese see this as derogitory given their strong beilief that because they watched some anime that all the sudden they are japanese.
This is a high-context word, in the american dialect, given the type of people using the word and the context of the discussion this OTAKU could mean expert or geek, complemetary or derogatory.

The Urban Dictionary T-Shirt

My definition, which was correct was removed by biased peoples. Oh well. Here I go again.

In Japan the word Otaku is a label that is quite bad. Most Japanese people would not want to be considered an otaku.
In America, however, we have morphed the word as we always do to our own meaning. There is nothing wrong with this. Over in America it means "to be a big fan of", and really doesn't have a bad meaning, as it would in Japan.

As such, you wouldn't want to go to Japan and start saying how much of an Otaku you are. In America this is fine, and probably in Canada as well. However, alot of people here seem to forget that they are saying what the Japanese interpret it as. Most people that read this hail from North America where the definition has a fairly benign meaning.

The Urban Dictionary T-Shirt

JAPAN:In Japanese was "Otaku" very polite form of "you" (literally your house). During the time the meaning has changed to hardcore fan of something usually manga and anime. Otaku has became used in meaning : nerd or jerk. Nowadays in Japan is the meaning returning back to non-offensive usage because of econimic trends.

ELSEWHERE: Out of Japan is the term "Otaku" used in the meaning of hardcore fan of anime and Manga. Many of anime fans call themselves otaku despite knowing it's meaning in Japan.